I usually go for a count of 200, then do crunches/squats/kettle bell squats depending on how dead I feel, something intermediate, usually stairstep, then another 200. Being in generally shitty shape, that kicks my ass in a short time, which is good, because my morning workout time is limited. To each their own, I guess.

I like to do just a few minutes of jumping rope before hitting the bag, to warm up and set the tone for moving lightly on the balls of the feet. Then, I like to finish with skipping rope again, until I'm good and tired after I'm done with bagwork.

I agree. I think for someone just starting out, keeping moving is in the most important thing. Not how fast they are when they're jumping or exercising. That helps them to get a feel for the movement, build up their coordination, tone and strength. Then, as they get more comfortable, just increase the speed slightly and add a few more reps. You wouldn't want your body to get use to resting each time after "burst" mode. When i'm working out with my son, I usually tell him when he's winded, keep doing everything, but slow waaaay down.

As someone who is good at skipping but once sucked I insist that you don't count. Use a round timer if you can only skip 10-12 times so what. Restart and keep skipping to the end of the round. Counting will make you inappropriately aware of the rope and it will make you feel like you are skipping forever. You shouldn't be thinking about counting you should be thinking about moving and rhythm.

After years and years I still kinda suck at skipping so my advice may not be any good but...
Try focusing on a spot on the wall straight ahead and keep the height of your jumps(more like bounces) to a minimum.

As someone who is good at skipping but once sucked I insist that you don't count. Use a round timer if you can only skip 10-12 times so what. Restart and keep skipping to the end of the round. Counting will make you inappropriately aware of the rope and it will make you feel like you are skipping forever. You shouldn't be thinking about counting you should be thinking about moving and rhythm.

That's an interesting and valid point.
I was just recounting how i was taught, but i totally get what you're saying now.